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Hey Mate
your answer is ----
firstly we find roots of 2x^2+x-1
2x^2+x-1 = 0
=> 2x^2+2x-x-1 = 0
=>2x(x+1) -(x+1) = 0
=> (x+1) (2x-1) = 0
=> x = 1/2 or -1
Let f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1 only when
f(-1) = 0 or f(1/2) = 0
now , put x = 1 in f(x)
= 4×-1^4-2× -1^3 -6× -1^2 -1 +1
= 4+2 - 6 -1 +1
= 6 -6
=0
so, f(-1) = 0
hence, f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1
HOPE IT HELPS YOU
your answer is ----
firstly we find roots of 2x^2+x-1
2x^2+x-1 = 0
=> 2x^2+2x-x-1 = 0
=>2x(x+1) -(x+1) = 0
=> (x+1) (2x-1) = 0
=> x = 1/2 or -1
Let f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1 only when
f(-1) = 0 or f(1/2) = 0
now , put x = 1 in f(x)
= 4×-1^4-2× -1^3 -6× -1^2 -1 +1
= 4+2 - 6 -1 +1
= 6 -6
=0
so, f(-1) = 0
hence, f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1
HOPE IT HELPS YOU
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